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Compensating wage differentials and the optimal provision of unemployment insurance.

I. Introduction

Between 1970 and 1987 the number of workers covered by unemployment insurance nearly doubled,(1) and benefit payments increased from $3.8 billion to $14.2 billion annually. Economists attribute this increased coverage in part for the sizable increase in the long-run (natural) unemployment rate over the same period |17~. The adequacy of unemployment insurance benefits is a major social and political concern, with repercussions extending to individual welfare and to the profits and productivity of American industries. Yet there has been no statistical investigation to test the adequacy of benefit levels, or to determine the net financial burden on firms, taking the wage offset for benefits into account.

Viscusi and Moore |22~ developed a test for the optimality of social insurance benefits based on the tradeoff between wages and workers' compensation benefits. Their argument states that if benefit levels were adequate, individuals would be willing to trade wages for benefits at an actuarially fair rate, adjusted for the level of insurance loading. If benefits were too low, individuals would be willing to forego more than the efficient amount of wages to increase the level of insurance. If benefits were excessive, an individual would not be willing to pay the efficient rate in exchange for increased coverage. This paper evaluates unemployment insurance benefits using a parallel approach, with further attention given to moral hazard considerations, and using an alternative risk measure that accounts for the average duration of unemployment spells as well as their frequency. The results of this research estimate the price that workers would pay to insure their income against unemployment in the presence of an efficient (competitive) insurance market. That price provides a reference point for implicit insurance rates as established under the existing unemployment insurance program. Related studies have considered the effect of unemployment insurance on wages. Topel |19~ used the pooled 1977-80 Current Population Surveys to estimate the impact of unemployment risk on wages, controlling for unemployment insurance (UI) benefits, as well as the effect of UI on the propensity for agents to enter and leave spells of unemployment (on which a large literature exists). He did not, however, evaluate insurance levels in regard to their optimal rates, or consider the net cost of the unemployment insurance system. Abowd and Ashenfelter |1~ estimated compensating wage differentials for anticipated unemployment risk using the Panel Study of Income Dynamics. Their study included UI benefits as a substitute for wages in the calculation of the effective hours of employment, without including them explicitly in the wage equation.

Previous efforts to determine the adequacy of unemployment insurance evaluated benefit levels based on their effect on individuals' lifestyles. In one such study, the U.S. Department of Labor |20~ interviewed 1650 Arizona residents after 5, 13 and 25 weeks of compensated unemployment in order to measure changes in household composition, nonbeneficiary household income, "necessary and obligated" expenditures, reservation wages, savings, and outside assistance received. Although the welfare of social insurance recipients is of critical concern, it is unclear how to judge benefit levels with respect to the lifestyle adjustments they impose, and efficiency considerations are absent from such criteria.

Section II of this paper outlines the structure of the unemployment insurance system. Section III derives the theoretically optimal wage-benefit tradeoff. Section IV describes the empirical analysis. Section V reports the results and discusses their implications. Section VI concludes the paper.

II. Unemployment Insurance Policies and Benefit Availability

The federal-state system of unemployment insurance was established under the Social Security Act of 1935. Among social insurance programs it is second only to Old-Age, Survivors, Disability, and Health Insurance (OASDHI) in the extent of its coverage. Individual states are free to adapt their programs to suit their particular needs, and consequently, no two state laws are alike. Each state determines UI benefit levels based on the earned income of workers subject to minimum and maximum benefit amounts. Benefit ceilings are justified on the grounds that high-income workers should be better able to finance themselves during periods of unemployment |13~. Maximum benefit levels are so low, however, that the earnings of a majority of eligible workers in the 1986 Current Population Survey qualified them to receive the maximum benefit amount. Thus, most workers are paid on what is effectively a flat-rate basis. For workers whose earnings put them between the minimum and maximum benefit amounts, benefits range from 50-60 percent of their average weekly earnings, often measured over the quarter during which earnings were the highest.

In 1988, state programs paid $12.6 billion in unemployment benefits. In the formal analysis that follows, it is assumed (for simplicity) that employers bear the full burden of the unemployment insurance costs incurred by their employees--a reasonable approximation of reality in most cases. Benefit payments are financed by employer contributions based on the first $7000 paid to each worker in a calendar year. In order to properly allocate the cost of unemployment benefits, every state determines employers' contribution rates based on an experience rating formula. As an example, 32 states use the reserve-ratio formula, under which the difference between an employer's contributions to the state benefit fund and the benefits received by that employer's workers is divided by their payroll to determine their reserve-ratio. Contribution rates are then assigned with an inverse relation to reserve-ratios. This formula is designed to insure that no employer will be granted a rate reduction unless the employer's total past contributions to the fund exceed total benefit payments to his or her workers.

The administrative costs of the unemployment insurance system are covered in full by federal grants to the states, and financed with the 0.8 percent Federal Unemployment Tax. Thus all employee contributions to the UI system go towards benefit payments in that state. The total expenditure on unemployment insurance administration in 1988 was $1.6 billion, resulting in an average cost of 13 cents per dollar of benefits paid to employees.
Table I. Unemployment Rate Ranges for Major Industries 1980-87


Agriculture 10.5-16.0
Mining 6.4-17.0
Construction 11.6-18.4
Manufacturing 6.0-11.2
Transportation/Public Utilities 4.5-7.4
Wholesale/Retail Trade 6.9-10.0
Finance, Insurance, Real Estate 3.1-4.5
Services 5.4-7.9
Government 3.5-5.3

As unemployment insurance benefits are a valued component of worker compensation, we should expect accompanying compensating wage differentials.(2) The plausibility of workers taking UI benefits into account in their employment decisions is supported by the figures in Table I, which indicate the range of unemployment rates in nine major industries over the 1980-87 period. As many as one-sixth of the workers in less stable industries were unemployed at any given time, and the average unemployment spell lasted 15.3 weeks. The variability in maximum and minimum benefit levels across states is evident in Table II, where benefit limits for 1989 are seen to differ by over 100 percent. Although the considerable variance in state UI benefit levels may induce workers in high unemployment industries to shop across states for a preferred wage-unemployment risk-benefit bundle, interstate migration is not necessary to allow workers to experience the wage-benefit tradeoffs discussed in this paper. Within a given state, jobs with differing wage and job-security levels will be within the workers' choice set. The expected replacement rate |risk*(benefits/wages)~ varies with wage and risk to produce the same effect as an increase in the benefit level, holding wage and risk constant.(3) The wage response to changes in the expected replacement rate can then be used to estimate the dampening effect of UI benefits on the compensating wage differential for unemployment risk.
Table II. State Unemployment Insurance Benefit Ranges

 Minimum Maximum Minimum
 Weekly Weekly Weekly
Weekly State Benefit Benefit State Benefit

Alabama 22 145 Montana 46 185
Alaska 38 260 Nebraska 20 134
Arizona 40 145 Nevada 16 184
Arkansas 37 209 New Hampshire 39 156
California 30 166 New Jersey 51 258
Colorado 25 214 New Mexico 33 166
Connecticut 15 284 New York 40 180
Delaware 20 205 North Carolina 19 228
Florida 10 200 North Dakota 43 183
Georgia 37 165 Ohio 42 268
Hawaii 5 239 Oklahoma 16 197
Idaho 44 193 Oregon 53 229
Illinois 51 244 Pennsylvania 35 274
Indiana 40 161 Rhode Island 48 300
Iowa 26 214 South Carolina 20 147
Kansas 52 210 South Dakota 28 140
Kentucky 22 166 Tennessee 30 155
Louisiana 10 181 Texas 34 210
Maine 29 256 Utah 14 208
Maryland 25 205 Vermont 31 169
Massachusetts 14 382 Virginia 56 176
Michigan 59 263 Washington 57 209
Minnesota 38 254 West Virginia 24 225
Mississippi 30 145 Wyoming 36 200
Missouri 33 150

III. Conceptual Framework

This paper defines the optimal level of UI benefits as that which would exist in the presence of an efficient insurance market. This privately optimal level of insurance may differ from the socially optimal level due to positive externalities associated with the accommodation of unemployed workers.(4) If insurance were diminished, unemployed workers might become greater financial and emotional liabilities to their communities, and require alternative forms of assistance. For this reason, the privately optimal provision of benefits discussed here should be considered as a lower bound for the socially optimal level of provision.

In order to evaluate current levels of unemployment insurance benefits, it is first necessary to find the efficient tradeoff between wages and benefits for comparison with empirically determined implicit insurance prices. Using a modification of the health state utility function approach of Viscusi |21~, the efficient substitution between these compensation components can be derived in a utility maximizing framework. The efficient rate can then be used as a reference point for tradeoffs exhibited in empirical results to determine whether or not current benefit levels are appropriate.

This study uses data from 1984-86, at which time benefits were taxed differently from income(5) (that is no longer the case). The notation |t.sup.b~ and t will be used to represent the marginal tax rates on benefits and wages, respectively. Consider utility as a function of income and leisure, the levels of which depend on whether the worker is in a state of employment or unemployment. In an employed state, the worker works h hours per week, earns after-tax wages w = W(1 - t) per week, and experiences utility |U.sup.e~ = U(w, h). In an unemployed state, the worker searches for employment for s hours per week (s |is less than~ h), earns after-tax unemployment insurance benefits b = B (1 - |t.sup.b~), and experiences utility |U.sup.u~ = U(b, s). Let unemployment risk p be the anticipated fraction of time spent unemployed in the worker's state and industry in the given year. In order to incorporate the administrative costs of the unemployment insurance system, allow a to represent the loading cost per dollar of expected unemployment benefits. Moral hazard presents an additional cost to be considered in the computation of optimal wage-benefit tradeoffs. Previous studies have found the level of unemployment benefits to effect both the probability and the duration of unemployment. Estimates of the increase in unemployment duration resulting from a ten percentage point increase in the UI replacement rate are generally between one-half and one and one-half weeks.(6) In terms of the incidence effect, the estimates of Feldstein |181~ imply that a 10 percent increase in the benefit replacement ratio would raise the predicted temporary layoff unemployment rate by about 0.1 percentage points, and in two related studies of male workers only, Topel |18; 19~ estimated that such a benefit increase would increase the temporary and permanent unemployment rates by about 0.6 and 0.2 percentage points respectively. Estimates of the moral hazard cost per dollar of benefits (m) are calculated based on these estimates.(7) Other studies belittle the potential damage from moral hazard. Ben-Horim and Zuckerman |4~ argue that unemployment insurance benefits could decrease the expected duration of unemployment benefits by providing financial resources with which to intensify the job search. And Burgess and Kingston |6~ find that increased unemployment duration due to UI support may reflect workers' ability to resist financial pressures and hold out for a more stable and productive position.

Following Viscusi and Moore |22~, the optimal tradeoff between wages and benefits is obtained by maximizing the worker's expected utility subject to a zero profits constraint for the firm, and substituting the result into the equation for the welfare-preserving tradeoff. The outcome is

dw/db = -|p(1 + a + m)(1 - t)~/|(1 - p)(1 - |t.sup.b~)~. (1)

The efficient rate of tradeoff between wages and unemployment insurance benefits is thus the negative of the ratio of the probabilities of being unemployed and employed weighted by functions of the marginal tax rates, moral hazard costs, and the loading factor. As each of these elements is observable, the theoretical optimum can be calculated and compared to empirically observed rates of tradeoff. This expression differs from the efficient tradeoff between wages and workers' compensation benefits reported by Viscusi and Moore by the inclusion of moral hazard costs (m) and the marginal tax rate on unemployment benefits (|t.sup.b~), and by the netting-out of income taxes for a more accurate comparison to the empirical tradeoff between after-tax wages and benefits.

IV. Empirical Estimation of the Hedonic Wage Equation

The micro-level data for this research comes from the 1986 Current Population Survey (CPS). Data from the 1984-86 waves of the University of Michigan Panel Study of Income Dynamics are used to test the robustness of the results. The CPS data collected by the Bureau of the Census provide a large, representative sample for labor market analysis. The data omits a job tenure variable, for which this research substitutes an experience variable constructed as age minus years of education minus six. The sample period of 1984-86 was one of fluctuating UI payments and decreasing tax deductibility of benefits, resulting in variation in the real, after-tax benefit levels within states, in addition to the variation that exists between states. The CPS subsample used here contains approximately 25,000 observations per year on individuals over the age of sixteen who had worked at least thirty hours per week during the previous year, and were either employed or unemployed on the survey date. Individuals were excluded from the sample if they were self-employed, or worked in the public, household, or agricultural sectors, because they were not eligible for state unemployment benefits. The PSID data sample consists of 2500 heads of household who otherwise have demographics similar to those in the CPS sample. The PSID data does include a job tenure variable which was used in the estimation.

Central to this study are the unemployment risk and benefit variables. Unemployment risk is estimated for each two-digit standard industrial classification code within each state and year as the average number of unemployed workdays per year divided by the total number of workdays in a year in the absence of unemployment. The risk variable can thus be interpreted as the fraction of time that an individual in a particular industry, state, and year can expect to be unemployed. This measure of risk, as opposed to the probability of an unemployment spell, incorporates the effects of the duration of unemployment spells, and provides a unit-less variable to facilitate the analysis.

Abowd and Ashenfelter |1~ and most other previous studies used UI replacement ratios based on an industry average benefit level,(8) whereas actual benefits rely directly on workers' wages TABULAR DATA OMITTED and the number of dependents. The present study calculates individual-specific benefit levels and replacement rates based on the unemployment benefits that each individual would collect in the event of an unemployment spell. These values are calculated using state unemployment benefit formulas in conjunction with data on the worker's income and number of dependents. The after-tax benefit levels used here account for the preferential taxation of UI benefits for low income individuals that existed prior to 1987. The UI replacement ratio is formed by dividing the worker's potential weekly after-tax benefit level by his or her after-tax weekly wage:(9)

|R.sub.i~ = after-tax benefits/after-tax weekly wage. (2)

In the wage equations below, the replacement ratio is weighted with the risk variable to create a measure of the expected replacement ratio. The interaction of risk with the replacement ratio is appropriate because the importance of benefits is proportional to the risk level, and when there is no risk, the replacement rate is meaningless. Table III provides a complete list of variable definitions.
Table IV. Sample Means and Standard Deviations (N = 24,871)

Variable Mean Standard Deviation

WAGE 5.474 2.930
RISK 0.0433 0.0476
LOST WORKDAYS 72.910 61.201
HOURS PER WEEK 42.775 8.127
FEMALE 0.379 0.485
NON-WHITE 0.112 0.316
EXPERIENCE 18.594 12.432
HIGH SCHOOL 0.408 0.491
HIGH SCHOOL PLUS 0.234 0.424
CENTRAL CITY 0.242 0.691
MSA NON-CENT. CITY 0.351 0.491
UNION CONTRACT 0.045 0.183
NORTHEAST 0.104 2.042
NORTH CENTRAL 0.205 0.404
SOUTH 0.386 1.038
MARRIED 0.659 0.476
OCCUPATION0 0.186 0.548
OCCUPATION1 0.043 0.202
OCCUPATION2 0.126 0.332
OCCUPATION3 0.147 0.354
OCCUPATION4 0.091 0.288
OCCUPATION5 0.118 0.323
OCCUPATION6 0.057 0.232
OCCUPATION7 0.102 0.303
OCCUPATION8 0.097 0.296

The dependent variable in the wage equations is either the worker's after-tax hourly wage or its natural logarithm. The independent variables include a vector of personal characteristics including sex, race, experience, education, geographical region, and city size dummy variables. Occupational dummy variables control for unmeasured occupation-specific characteristics, and a union dummy variable takes into account the wage effect of operating under a union contract. Industry health risks are included using a measure of the annual lost workdays due to illness or injury. Table IV summarizes the means and standard deviations of the variables. The sample is broadly representative of the labor force at large.

Estimates of the wage-benefit tradeoff are made using regressions of the hedonic wage equation. A worker-firm match occurs when a worker's indifference curve and a firm's isoprofit curve are both tangent to the common wage-attribute (hedonic) locus. The slope of the hedonic wage locus with respect to a given job attribute (e.g., risk or benefits) at any point represents the trade-off that workers at that point are willing to make between wages and that attribute.(10) The standard semi-logarithmic form serves as the basis for estimation, where X is a vector of productivity-related characteristics, p is the probability of unemployment, r is the physical injury rate for the job, and R is the agent's potential UI replacement ratio. The hedonic wage equation is estimated in the following forms: ln(|WAGE.sub.i~) = B|X.sub.i~ + ||Delta~.sub.1~|p.sub.i~ + ||Delta~.sub.2~|r.sub.i~ + ||Delta~.sub.3~|R.sub.i~|p.sub.i~ + ||Epsilon~.sub.i~, (3)

ln(|WAGE.sub.i~) = B|X.sub.i~ + ||Delta~.sub.1~|p.sub.i~ + ||Delta~.sub.2~|r.sub.i~ + ||Epsilon~.sub.i~, (4)


|WAGE.sub.i~ = B|X.sub.i~ + ||Delta~.sub.1~|p.sub.i~ + ||Delta~.sub.2~|r.sub.i~ + ||Delta~.sub.3~|R.sub.i~|p.sub.i~ + ||Epsilon~.sub.i~. (5) Equation (3) is the primary relation to be estimated, as it regresses log wages on all of the relevant variables including the weighted replacement ratio. Equation (4) estimates the unemployment coefficient while omitting UI benefits to study the consequence of failing to consider the effect of UI in reducing compensating differentials for risk. Equation (5) is estimated using wage rather than log wage as the dependent variable, a distinction which is theoretically arbitrary. In addition to these specifications, experiments that included the replacement rate in absolute terms, the square of the expected replacement rate, the square of the unemployment risk, and each of the squares and cross terms of the personal characteristics were run and found to make no substantive contribution to the estimation. Thus, only the simpler forms are reported here.

The specifications above have evolved from the log earnings functions of Mincer |11~, Becker |3~ and others. Abowd and Ashenfelter |1~ estimate compensating wage differentials for anticipated unemployment using equations that include the sample average UI replacement rate by industry, with the addition of lagged wages. Topel |19~ used a variant of equation (3) in his study of the wage effects of temporary and permanent layoff risk, differing primarily in its separate terms for the two types of layoff.

V. Compensating Differential Estimates

The empirical analysis focuses on the estimation of equation (3) in several variations. Table V summarizes the results of this estimation performed using 1986 CPS data. As expected, wages are higher for workers who are male, white, better educated, living in a large city, working in relatively dangerous industries, or working under a union contract. Wages increase at a decreasing rate with experience, and are higher in the Northeast and West than in the South and Midwest. The coefficient on the risk-weighted replacement rate, -2.037, is similar to Topel's estimated coefficients of -2.423 and -5.224 on the replacement rate weighted by the risks of permanent and temporary layoff respectively |19, 517~. All of the coefficients are statistically significant at the 95 percent level of confidence.

Table VI summarizes the compensating wage differentials for risk and unemployment insurance benefits. Regressions 2, 3, 6, and 7 test the sensitivity of the results to the specification of the regression equation and the data sample used. The OLS regression (6) indicates that using the instrumental variables estimator for risk does not serve to misrepresent the relationships in question. The coefficient on risk is positive, the wage-benefit tradeoff is negative, and although the results are biased, they are highly significant. To verify the legitimacy of using log wage as the dependent variable, regression 7 replicates regression 1 using wage as the dependent variable, and produces analogous results. Occupational dummy variables are omitted in regression 3 as an additional test of robustness, yielding somewhat larger risk and benefit coefficients, but again no substantial change in the results.
Table V. Estimates of Log Wage Equation

Variable Coefficient t-ratio

RISK 0.742 1.89
RISK X REPL. RATE -2.037 -2.34
LOST WORKDAYS 0.000266 5.88
FEMALE -0.291 -47.08
NON-WHITE -0.054 -6.86
EXPERIENCE 0.019 25.66
EXPERIENCE SQUARED -0.000310 -20.55
HIGH SCHOOL -0.214 -26.69
HIGH SCHOOL PLUS -0.152 -19.22
CENTRAL CITY 0.054 8.72
MSA NON-CENT. CITY 0.078 14.10
UNION CONTRACT 0.182 13.54
NORTHEAST -0.012 -3.06
NORTH CENTRAL -0.017 -2.71
SOUTH -0.045 -8.84
OCCUPATION0 0.028 2.05
OCCUPATION1 -0.126 -7.22
OCCUPATION2 -0.156 -10.89
OCCUPATION3 -0.120 -8.42
OCCUPATION4 -0.289 -18.46
OCCUPATION5 -0.064 -4.28
OCCUPATION6 -0.029 1.77
OCCUPATION7 -0.135 -8.89
OCCUPATION8 -0.166 -10.82


The findings support the hypothesis that UI encourages sporadic employment patterns by providing work-free income for unemployed workers. Although UI benefits are typically terminated after 26 weeks, in 1986 the average worker was re-hired or found new employment in 15.3 weeks, and more than 85 percent of unemployed workers received benefits for the duration of their unemployment (excluding the one week waiting period present in 39 states). The estimated coefficients from each of the regressions indicate that the prospect of income without labor brings employees to accept a somewhat lower wage in industries that involve higher unemployment risk, given the availability of unemployment insurance. The negative and significant effect of risk on wages (evaluated at the mean replacement rate) suggests that individuals may prefer to receive a reduced salary for the compensable period of unemployment rather than receiving their full salary and working. This is not the case for industries with higher injury risk, in which case workers' compensation benefits are received while in a state of disability |21~.

Unemployment benefits act to diminish the danger of income loss. When benefits are not accounted for in the wage equation, the negative effect of benefits on the compensation for risk is absorbed into the risk coefficient. A comparison of regressions 1 and 4 demonstrates that when benefits are omitted from the wage equation, the negative wage-risk tradeoff can be overestimated. The wage-risk tradeoff found in regression 1 is calculated as 0.74 - 2.04(0.429) = -0.13, where 0.429 is the average replacement rate. This 13 percent tradeoff is smaller than the 17 percent tradeoff estimated using regression 4. This result is sustained using the PSID data in regressions 2 and 5.

The hypothesis that compensating wage differentials exist for UI benefits cannot be rejected at the 95 percent level of confidence for any of the equations. The dollar amount that workers are willing to forego per week in order to receive an additional dollar of weekly benefits when unemployed is found by solving equation (3) for the wage-benefit tradeoff:

40(dw/db) = ||Delta~.sub.1~p/|1 + ln(WAGE) - BX - ||Delta~.sub.1~p - ||Delta~.sub.2~r~. (6)

Evaluated at the mean values of the variables, this calculation indicates that an additional dollar of benefits leads to a $.09 decrease in wages. In the absence of significant moral hazard problems, the efficient tradeoff based on equation (1) would be $.05 per dollar of benefits, and the discrepancy between the actual and efficient rates of tradeoff would indicate that existing benefit levels are suboptimal. When the moral hazard cost per dollar of benefits is included in the calculation of the efficient benefit level as described in section III, the efficient tradeoff is found to be close to the empirical tradeoff. Based on the range of common duration effect estimates discussed above, the efficient tradeoff is between $.07 and $.08 per dollar of benefits using Feldstein's incidence effect estimates |8~, and between $.10 and $.11 using Topel's estimates |19~. The actual tradeoff falls between these ranges, suggesting that unemployment benefits approximate the optimal level. Table VII presents the ratio of the empirical tradeoff to the efficient tradeoff for subgroups within the sample.(11) A ratio greater than one suggests that UI benefit availability is below the efficient level for that group, whereas a ratio less than one indicates a possible excess of benefits. None of the states provide notably inadequate benefits, whereas the states of Alaska, Louisiana, West Virginia and Wyoming appear to provide more than the optimal level of insurance. Benefit levels are more satisfactory for men and less educated workers than for women and better educated workers, respectively. This may result from members of the former groups generally holding less-stable positions in which it is efficient to forego a larger portion of wages in exchange for more substantial insurance coverage. Predictably, unemployment rates decrease with educational attainment, and although the unemployment rate for males trailed that for females for most of the past decade, around 60 percent of unemployed males each year have been job losers, while a similar majority of females have been new entrants, reentrants, and job leavers. Thus, an efficient insurance market would command higher UI prices from men and better educated workers. The empirical data indicate that these groups are insured to such a degree that they would be unwilling to pay the higher actuarially fair price for additional insurance.
Table VII. Empirical/Efficient Wage-Benefit Tradeoffs

Group Efficient Tradeoff

Women 1.00
Men 0.99
Non-White 0.99
White 0.99
Less Than High School 0.97
High School 0.99
High School Plus 1.00
College 0.99
Alabama 0.97
Alaska 0.95
Arizona 0.99
Arkansas 0.99
California 0.99
Connecticut 1.02
Delaware 1.01
Florida 1.00
Hawaii 1.00
Indiana 0.99
Iowa 0.98
Kansas 1.03
Kentucky 0.96
Louisiana 0.95
Maine 0.99
Maryland 1.01
Michigan 0.99
Minnesota 1.00
Mississippi 0.97
Missouri 0.98
Montana 0.98
Nebraska 1.01
Nevada 0.97
New Mexico 0.96
New York 1.00
North Carolina 1.01
Oklahoma 0.97
Oregon 0.96
Rhode Island 1.01
South Carolina 1.00
Tennessee 0.98
Utah 1.00
Vermont 1.01
Virginia 1.00
Washington 0.97
West Virginia 0.92
Wyoming 0.94

VI. Conclusions

Almost since its inception in 1935, the federal-state unemployment insurance program has been criticized for providing inadequate benefits. Substantial increases in benefit levels since the 1970s appear to have corrected past deficiencies. This paper presents empirical evidence that UI benefits approximate the level that would exist if an efficient unemployment insurance market were available. The average wage offset for UI benefits is approximately equal to the cost of their provision, taking moral hazard and administrative costs into account. The typical firm should thus be indifferent to the existence of the unemployment insurance system. Given current unemployment insurance replacement rates, compensating differentials for unemployment risk are shown to be negative and significant, suggesting that the prospect of insured unemployment is preferred over work for correspondingly higher pay. 1. Covered employment increased from 56 to 104 million, representing an increase from 67 to 86 percent of the work force.

2. Suppose that the indirect utility of a worker depends on unemployment risk (p), hours (h), after-tax wages (w), and benefits (b). If two jobs with equivalent risk levels and hours are available in two states with differing benefit levels |b.sub.high~ and |b.sub.low~, then for the same wages, workers would always prefer employment in the job offering higher benefits |b.sub.high~. The labor market will operate to equalize the utility level provided by the two jobs by providing higher wages in the job with lower benefits, so that V(|w.sub.high~, p, h, |b.sub.low~) = V(|w.sub.low~, p, h, |b.sub.high~).

3. Consider a worker choosing between two jobs differing only in unemployment risk (p) and after-tax wage (w). The relatively secure job offers w = $200 and (for simplicity) p = 1, and the less secure job offers w = $250 and p = 2. Suppose that both wage levels would bring the worker to the maximum benefit level of $100. In this case the risk-weighted replacement rate for the more secure job is 100/200, and for the less secure job it is 2(100/250) = 2(80/200) = (160/200). It is evident that doubling the risk level has the same effect on the risk-weighted replacement rate as doubling the benefit level, and increasing wages by 50 is equivalent to decreasing the benefit level by one-fifth.

4. The negative moral hazard effects are incorporated into the analysis below.

5. For example, in 1982-86, UI benefits were included in gross income if the sum of the worker's adjusted gross income and the UI benefits for the year exceeded $18,000 in the case of a joint return, zero in the case of a married worker filing separately, and $12,000 for all other workers. In these cases one-half of the excess up to the amount of benefits received was included in the workers gross income.

6. In response to a ten percentage point increase in the replacement rate, Meyer |10~ estimates an increase in duration of about one and one-half weeks. Ehrenberg and Oaxaca |7~ find similar results for middle-aged men, and increases of 0.3, 0.2, and 0.5 weeks respectively for middle-aged women, young men, and young women. The estimates of Solon |16~, Topel |19~, Moffitt and Nicholson |12~, and Kiefer and Neuman |9~ also imply increases in mean durations of one-half to one full week resulting from a ten percentage point increase in the replacement rate.

7. To calculate the moral hazard cost due to the duration effect, note that a $1.00 increase in expenditures on benefits represents a 0.0773 percent increase in the average replacement rate for one worker for the average duration of an unemployment spell (15.3 weeks). If a ten percentage point (25 percent) increase in the replacement rate from 0.4 to 0.5 would increase spell duration by one week, for example, then the $1.00 expenditure will lead to an increase in spell duration by 0.0773/25 = .00309 weeks. With average weekly benefits of $84.5 after the benefit increase, this represents an additional cost of $0.261. To measure the cost of the incidence effect using Feldstein's |8~ estimates (for example), note that a $1.00 increase in benefit expenditures would (on the average) fund a 0.0773 percent increase in the replacement rate for one unemployment spell, leading to an increase in the unemployment rate of 0.0773*(0.1/10) = 0.000773 percentage points for all those eligible for the increase. Given that the unemployment rate in the sample is 3.892 percent without the benefit increase, there will be 1/(0.00000773 + 0.03892) = 25.7 workers out of which one can expect to become unemployed and receive the higher replacement rate for the average length of an unemployment spell. The increase in unemployment (measured as the fraction of an unemployment spell) resulting from a one dollar increase in benefit expenditures is thus 25.7 x .00000773 = 0.000194. The moral hazard cost due to the increased incidence of unemployment is 0.000194 multiplied by the average total benefit expenditure on an unemployment spell (15.3 weeks multiplied by $84.5 benefits/week = $1292.85), which equals $0.257. In the analogous calculation based on Topel's findings, an incidence-weighted average of the UI effects on temporary and permanent unemployment was used.

8. Exceptions include Topel |18; 19~.

9. Because the inclusion of after-tax wages renders |R.sub.i~ endogenous, |w.sub.i~ is imputed using a vector of right hand side variables and excluded instruments (e.g., the number of children, marital status, maximum and minimum benefit levels, and cross terms) prior to the calculation of the replacement rate. This method follows Topel |19~.

10. To the extent that worker preferences are alike, the hedonic locus approximates the workers' indifference curve. Individual heterogeneity and self-selection for jobs could result in significant biases that warrant attention in future research |5; 14; 15~.

11. The moral hazard cost used to calculate the figures in Table VII is based on a one week duration effect as the result of a ten percentage point increase in benefits, and an average of the incidence effects estimated by Feldstein |8~ and Topel |119~.


1. Abowd, John M. and Orley Ashenfelter. "Anticipated Unemployment, Temporary Layoffs, and Compensating Wage Differentials," in Studies in Labor Markets, edited by S. Rosen. Chicago: The University of Chicago Press, 1981.

2. Anderson, David A. Optimal Compensation Systems. Ann Arbor, Mich.: University Microfilms, 1992.

3. Becker, Gary S. Human Capital. Chicago: University of Chicago Press, 1975.

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Author:Anderson, David A.
Publication:Southern Economic Journal
Date:Jan 1, 1994
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